Solving for Angles in a Polygon

Q3W8: Word Problems Involving Sides and Angles of Polygon

By Shin Baquirin

Learning Objectives

At the end of this lesson, the learner should be able to solve problems involving sides and angles of a polygon.

​ (M7GE-IIIj-1)

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Open Ended

Activity:

Try to look around you, have you seen any object or thing from your surrounding that is/are related to Geometry specifically in polygons? If yes, please cite examples as many as you can.

Open Ended

Knowing that geometry is everywhere, do you agree that Mathematics is applicable in real-life situation? Why or why not?

Multiple Choice

What is a polygon?

• An open figure made up of segments.

• A closed figure that can be formed with at least three segments connecting their endpoints.

• Is a close curved figure.

• a figure with 100 side

​Polygon

The word polygon came from the Greek words "poly" which means "many" and "​gonia", which means "angles"

Subject | Subject

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Multiple Choice

What is the sum of the interior angle of a undecagon?

• 11

• 1,620

• 1,980

• 147.27

180 (n-2) = 180(11-2) = ​180 (9) = 1620

Multiple Choice

What is the measure of one of the exterior angle of a regular 70- gon?

• 174.86

• 12, 240

• 5.14

• 68

Multiple Choice

Given that angle A and C measures 100 and 55 respectively, determine the measurement of angle B.

• 25

• 30

• 60

• 90

Draw

Given that angle A and C measures 100 and 55 respectively, determine the measurement of angle B.

100° + 55° + B = 180°​

155° + B = 180°​

B = 180°-155°

B= 25​°

Subject | Subject

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Multiple Choice

The interior angle of a pentagon can be expressed as p, 2p, 3p, 3p, 3p. What is the measure of the largest angle?

• $$45\degree$$  

• $$90\degree$$  

• $$135\degree$$  

• $$540\degree$$  

​Solution:

p + 2p + 3p + 3p + 3p + = 540

12p = 540

12p = 540​

12 12

​p=​ 45⁰

​

2p = 2(45⁰​) = 90⁰

3p = 3(45⁰​) = 135⁰

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The measure of the largest interior angle of the pentagon is 3p = 135⁰​

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Subject | Subject

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Multiple Choice

Mr. Salvador’s land is shaped like a pentagon. Two of the pentagon’s interior angles are right angles. The remaining three angles are congruent, what is the measure of each angle?

• $$90\degree$$  

• $$540\degree$$  

• $$120\degree$$  

• $$360\degree$$  

2 (right angles) + 3 (congruent angles​) = 540⁰

2 (90⁰​) + 3 (x) = 540⁰

​180⁰ + 3x = 540⁰​

3x = 540⁰​ - 180⁰

3x = 360⁰​

3x = 360⁰​

3 3

x = 120⁰​

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The ​measure of each congruent angles are 120⁰

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ASSIGNMENT!

Kindly visit our Google Classroom and answer Activity and Quiz #3.8. Then submit it on April 01, 3PM.

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